Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

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Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Question

Chapter 1.2, Problem 54E

(a)

To determine

To find:The quadratic regressionfor the datagiven in the table for the gross revenue of Broadway season.

(a)

Expert Solution

Answer to Problem 54E

The quadratic regression equation for the given data ofBroadway Season Revenue is y=0.723x2+26.726x+290.914 .

Explanation of Solution

Given information:The table given below shows the gross revenue for Broadway season in different years:

Broadway Season Revenue
Year	Amount ($ millions)
1994	406
1999	603
2004	769
2005	862
2006	939
2007	938

Calculation:

Consider that x=0 represents year 1999, x=1 represents year 2000, x=2 represents year 2001 and so on.

To find the natural logarithm regression equation of the given data, use graphing calculator.

Step 1: Press STAT1 keys to enter the given data.

Step 2: List the input values 4, 9, 14, 15, 16 and 17 in the L1 column.

Step 3: List the input values 406, 603, 769, 862, 939 and 938 in the L2 column.

Step 4: Press the keystrokes STAT⇒5ENTER to find line of quadratic regression and again press ENTER key.

y=0.723x2+26.73+290.914

Therefore, the quadratic regression equation for the Broadway Season Revenue is y=0.723x2+26.726x+290.914 .

(b)

To determine

To plot:The graph of the quadratic regression for the given data on a scatter plot.

(b)

Expert Solution

Explanation of Solution

Given information:The table given below shows the gross revenue for Broadway season in different years:

Broadway Season Revenue
Year	Amount ($ millions)
1994	406
1999	603
2004	769
2005	862
2006	939
2007	938

Graph:

From part (a), the quadratic regression equation for the Broadway Season Revenue is y=0.723x2+26.726x+290.914 . Now, to make the scatter plot, follow the steps using graphing calculator.

Step 1: Press 2ndY= and make sure that Plot 1 is ON. Choose the scatter plot icon in type.

Step 2: Press GRAPH key. Set the window at [0, 20] by [300, 1000] .

Step 3: Press the keystrokes STAT⇒5ENTER2nd1,2nd2,VARS⇒11ENTER and. Now, press the GRAPH key to plot the graph as shown below.

Calculus: Graphical, Numerical, Algebraic, Chapter 1.2, Problem 54E

Figure (1)

Interpretation: From the graph it can be observed that the gross revenue for Broadway season in year 2008 is more than 1000 millions of dollars.

(c)

To determine

To find: The amount of gross revenue for the Broadway Season in year 2012.

(c)

Expert Solution

Answer to Problem 54E

The amount of gross revenue for the Broadway Season in year 2012 is 1228.15 millions of dollars.

Explanation of Solution

Given information:The table given below shows the gross revenue for Broadway season in different years:

Broadway Season Revenue
Year	Amount ($ millions)
1994	406
1999	603
2004	769
2005	862
2006	939
2007	938

Calculation:

From part (a), the quadratic regression equation for the Broadway Season Revenue is y=0.723x2+26.726x+290.914 .

Consider that x=0 represents year 1999, x=1 represents year 2000, x=2 represents year 2001, x=17 represents year 2007and so on. The year 2012 is represented by x=22 .

Substitute 22 for x in the quadratic regression equation.

y=0.723(22)2+26.73(22)+290.914y=1228.15

Therefore, the amount of gross revenue for the Broadway Season in year 2012 is 1228.15 millions of dollars.

(d)

To determine

To find:The linear regression for the data given in the table for the gross revenue of Broadway season and the amount of revenue in 2012.

(d)

Expert Solution

Answer to Problem 54E

The linear regression equation for the Broadway Season Revenue is y=41.87x+229.48 and the approximate revenue in year 2012 is $1150 million.

Explanation of Solution

Given information:The table given below shows the gross revenue for Broadway season in different years:

Broadway Season Revenue
Year	Amount ($ millions)
1994	406
1999	603
2004	769
2005	862
2006	939
2007	938

Calculation:

To find the linear regression equation of the given data, use graphing calculator.

Press the keystrokes STAT⇒4ENTER .

y=41.87x+229.48

Now, substitute 22 for x in the above equation to find the revenue in 2012.

y=41.87(22)+229.48y=1150.62

Therefore, the linear regression equation for the Broadway Season Revenue is y=41.87x+229.48 and the approximate revenue in year 2012 is $1150 million.

Chapter 1.2, Problem 53E

Chapter 1.2, Problem 55E

Chapter 1 Solutions

Calculus: Graphical, Numerical, Algebraic

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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